#include <Eigen/Sparse>
#include <QImage>
#include <vector>

typedef Eigen::SparseMatrix<double> SpMat; // declares a column-major sparse matrix type of double
typedef Eigen::Triplet<double> T;

void
insertCoefficient(int id,
				  int i,
				  int j,
				  double w,
				  std::vector<T>& coeffs,
				  Eigen::VectorXd& b,
				  const Eigen::VectorXd& boundary)
{
	int n = int(boundary.size());
	int id1 = i + j * n;

	if (i == -1 || i == n)
		b(id) -= w * boundary(j); // constrained coefficient
	else if (j == -1 || j == n)
		b(id) -= w * boundary(i); // constrained coefficient
	else
		coeffs.push_back(T(id, id1, w)); // unknown coefficient
}

void
buildProblem(std::vector<T>& coefficients, Eigen::VectorXd& b, int n)
{
	b.setZero();
	Eigen::ArrayXd boundary = Eigen::ArrayXd::LinSpaced(n, 0, M_PI).sin().pow(2);
	for (int j = 0; j < n; ++j) {
		for (int i = 0; i < n; ++i) {
			int id = i + j * n;
			insertCoefficient(id, i - 1, j, -1, coefficients, b, boundary);
			insertCoefficient(id, i + 1, j, -1, coefficients, b, boundary);
			insertCoefficient(id, i, j - 1, -1, coefficients, b, boundary);
			insertCoefficient(id, i, j + 1, -1, coefficients, b, boundary);
			insertCoefficient(id, i, j, 4, coefficients, b, boundary);
		}
	}
}

void
saveAsBitmap(const Eigen::VectorXd& x, int n, const char* filename)
{
	Eigen::Array<unsigned char, Eigen::Dynamic, Eigen::Dynamic> bits = (x * 255).cast<unsigned char>();
	QImage img(bits.data(), n, n, QImage::Format_Indexed8);
	img.setColorCount(256);
	for (int i = 0; i < 256; i++)
		img.setColor(i, qRgb(i, i, i));
	img.save(filename);
}
